Digital filtering of signals after analog-to-digital conversion is necessary to extract the useful content from the signal processing information stream. In a typical application, only information content at a specific frequency of interest is useful. It is usually essential to filter out all frequency content other than the frequency of interest.
The convolution sum for a non-linear finite-impulse response (FIR) filter is of the form:N−1y(n)=Σb(i)x(n−i)i=0
Where:                y(n)=filter output for sample time n        b(i)=filter coefficients for filter of order N−1        x(n)=filter input at sample time n        N=number of filter taps        
A “folded” or “symmetric” FIR filter, for linear FIR filters, has the following form:ceil((N−1)/2)y(n)=Σb(i)[x(i)+x(n−1−i)]i=0
The latter format permits the filter tap counts to be doubled within the same timing and resources of a non-linear FIR, compared to the non-symmetric case.
Digital filtering in most of today's systems is done in a microprocessor (μP) or micro-controller, digital-signal processor (DSP), field-programmable gate array (FPGA), or a combination thereof. Digital filters required for precision extraction of desired signals from unwanted signals or noise are very computationally intensive, and quickly overwhelm the resources in DSP's or μP's. FPGA solutions require expensive, power-hungry devices and difficult, and custom-application design cycles Reprogramming the FPGA's as filter requirements change is also difficult. In addition, a unique design is required to interface to different processors or ADC's. The growth of remote, battery operated, sensor signal processing has exacerbated the problems.
Today's digital filtering requirements need a high-performance, easily programmable digital filter in a small, minimum pin-count, low-power, low-cost, and easy to integrate device. This requires a simple serial interface structure adaptable to modern DSP, μP, and ADC interfaces and easy-to-program digital filtering hardware. Emphasis on battery powered applications requires significant power reduction in all these devices.